Consider an incomplete pyramid of balls on a square base having 18 layers; and having 13 balls on each sideof the top layer. Then the total number N of balls in that pyramid satisfies(A) 9000 < N < 10000

(B) 8000 < N < 9000

(C) 7000 < N < 8000

(D) 10000 < N < 12000

Ans.

(B)

Sol.

Top layer has (13 13) balls similarly are layer below top layer will have (14 14) ballsWe have 18 layerSo total number of ballsN = (13)2 + (14)2 + ........ + (30)2N=

30 u 31 u 61 12 u 13 u 25

66

N = 8805.12.

A man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance istar road. For the remaining distance he takes a boat. His speed of traveling in mud , in water, on tar road is inthe ratio 3 : 4 : 5. The ratio of the durations he requires to cross the patch of mud, stream and tar road is1 4 5(A) : :(B) 3 : 8 : 15(C) 10 : 15 : 18(D) 1 : 2 : 32 3 2

Ans.

(C)

Sol.

Let distance is 6x

13.

Ans.Sol.

mud

tar

stream

distance

3x

2x

speed

3v

5v

4v

time

x3v

3x5v

2x4v

10

18

15

A frog is presently located at the origin (0, 0) in the xy-plane. It always jumps from a point with integercoordinates to a point with integer coordinates moving a distance of 5 units in each jump. What is theminimum number of jumps required for the frog to go from (0, 0) to (0, 1) ?(A) 2(B) 3(C) 4(D) 9(B)

(0, 6)5

II

III(4, 3)

4(0, 1)

5I

3 steps.

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14.

A certain 12-hour digital clock displays the hour and the minute of a day. Due to a defect in the clockwhenever the digit 1 is supposed to be displayed it displays 7. What fraction of the day will the clock showthe correct time ?(A)

12

(B)

58

(C)

34

(D)

56

Ans.

(A)

Sol.

The clock will show the incorrect time (between 1 2, 10 -11, 11-12 , 12 - 1 day and night both)

? in correct time 8 60 = 480 (each minute it will display 1)

There are 30 questions in a multiple choice test. A student gets 1 mark for each unattempted question, 0mark for each wrong answer and 4 marks for each corrent answer. A student answered x question correctlyand scored 60. Then the number of possible value of x is(A) 15

Ans.

(B) 10

(C) 6

(D) 5

(C)

Sol.Right

Wrong

Unattempted

(4 marks)

(0 mark)

(1 marks)

15

15

14

13

12

12

11

16

10

20

6 cases.

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PHYSICS16.

A simple pendulum oscillates freely between points A and B.

CA

B A

We now put a peg (nail) at some point C as shown. As the pendulum moves from A to the right, the stringwill bend at C and the pendulum will go to its extreme points D. Ignoring friction, the point D

Ans.

Sol.

(A) will lie on the line AB

(B) will lie above the line AB

(C) will lie below the line AB

(D) will coincide with B

(A)

A

According to law of conservation of mechanical energy

Ki + Ui = Kf + Uf0 + Ui = 0 + Ufhi = hfPoint D is at line AB

17.

A small child tries to moves a large rubber toy placed on the ground. The toy does not move but gets&deformed under her pushing force ( F ) which is obliquely upward as shown. Then

&Push F

&(A) the resultant of the pushing force ( F ), weight of the toy, normal force by the ground on the toy and the

frictional force is zero

(B) the normal force by the ground is equal and opposite to the weight of the toy&(C) the pushing force ( F ) of the child is balanced by the equal and opposite frictional force&(D) the pushing force ( F ) of the child is balanced by the total internal force in the toy generated due todeformation

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Ans.

(A)

Sol.

Fext

? asystem = 018.

A juggler tosses a ball up in the air with initial speed u. At the instant it reaches its maximum height H, hetosses up a second ball with the same initial speed. The two balls will collide at a height(A)

Ans.

H4

(B)

H2

(C)

3H4

(D)

3H4

(C)(1)

Sol.

H-hHh

(1) (2)

Hh=

1 2gt2

h = ut

1 2gt2

H = ut

..(1)

u22g

..(2)

t=

Hu(from (1) and (2))2g

?h=u

19.

3u 28g

u 1u2 gu 22g 24g3H4

On a horizontal frictionless frozen lake, a girl (36 kg) and a box (9 kg) are connected to each other by meansof a rope. Initially they are 20 m apart. The girl exerts a horizontal force on the box, pulling it towards her.How far has the girl traveled when she meets the box >

Ans.

(A) 10 m

(B) Since there is no friction, the girl will not move

(C) 16 m

(D) 4m

(D)

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Sol.

36kg20 m

9 kg

external force does not work on system

So according to concept of mass

36 x = 9 (20 x)x = 4m

20.

The following three objects (1) a metal tray, (2) a block of wood, and (3) a woolen cap are left in a closedroom overnight. Next day the temperature of each is recorded as T1, T2 and T3 respectively. The likelysituation is(A) T1 = T2 = T3

(B) T3 > T2 > T1

(C) T3 = T2 > T1

Ans.

(A)

Sol.

All the three object will be in thermal equilibrium then % T1 = T2 = T3.

21.

We sit in the room with windows open. Then

(D) T3 > T2 = T1

(A) air pressure on the floor of the room equals the atmospheric pressure but the air pressure on the ceiling isnegligible(B) air pressure is nearly the same on the floor, the walls and the ceiling(C) air pressure on the floor equals the weight of the air column inside the room (from floor to ceiling) perunit area(D) air pressure on the walls is zero since the weight of air acts downwardAns.

(B)

Sol.

Pressure of gas is app. same everywhere in the vessel

22.

A girl standing at point P on a beach wishes to reach a point Q in the sea as quickly as possible. She can runat 6 km h 1 on the beach and swim at 4 km h 1 in the sea. She should take the pathQsea

B C

beachP

(A) PAQAns.

(B) PBQ

(C) PCQ

(D) PDQ

(C)

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Sea

Sol.beach

In beach velocity is higher

? beach is rarer and sea is denser medium

So when it go from rarer to denser medium it bend toward normal to reach in minimum time.

23.

Light enters an isosceles right triangular prism at normal incidence through face AB and undergoes totalinternal reflection at face BC as shown below.B

The minimum value of the refractive index of the prism is close to

(A) 1.10Ans.

(C)

Sol.

i = 45 t C

(B) 1.55

(C) 1.42

(D) 1.72

For minimum refractive index C = 45

sin 45 = 1 = 2 = 1.42

24.

A convex lens is used to form an image of an object on a screen. If the upper half of the lens is blackened sothat it becomes opaque, then

Ans.

(A) only half of the image will be visible

(B) the image position shifts towards the lens

(C) the image position shifts away from the lens

(D) the brightness of the image reduces

(D)

Sol.

Only half part of the lens will be used so its intensity will be decreased25.

A cylindrical copper rod has length L and resistance R. If it is melted and formed into another rod of length2L, the resistance will be(A) R

Ans.

(B) 2R

(C) 4R

(D) 8R

(C)

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Sol.

Applying volume conservation

A L = A' 2LAA' =2ULR=AU u 2L U u 4L=R' =A'AR' = 4R

26.

Two charges + Q and 2Q are located at points A and B on a horizontal line as shown below

Ans.Sol.27.

Ans.Sol.

28.

+Q

2Q

The electric field is zero at a point which is located at a finite distance

(A) on the perpendicular bisector of AB(B) left of A on the line(C) between A and B on the line(D) right of B on the line(B)E1

E2

Q 2Q

A 750 W motor drivers a pump which lifts 300 litres of water per minute to a height of 6 meters. Theefficiency of the motor is nearly (take acceleration due to gravity to be 10 m/s2)(A) 30%(B) 40%(C) 50%(D) 20%(B)mgh = 300 10 6mgh 300 u 10 u 6Pi == 300 Wt60P0 = 750 W300 100 = 40 %K=750Figure below shows a portion of an electric circuit with the currents in amperes and their directions. Themagnitude and direction of the current in the portion PQ is3AP

1A

2A

8A4A

(A) 0AAns.

(B) 3 A from P to Q

2A

(C) 4 A from Q to P

(D) 6A from Q to P

(D)

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3AP2A

Q6A3

Sol.108A

29.

4A 1A6

4A

2A

214A nucleus of lead Pb 82emits two electrons followed by an alpha particle. The resulting nucleus will have

(A) 82 protons and 128 neutrons

(B) 80 protons and 130 neutrons

(C) 82 protons and 130 neutrons

(D) 78 protons and 134 neutrons

Ans.

(A)

Sol.

214Pb82 o X2e He 4

21082

82 o Proton210 82 = 128 Neutron

30.

The number of air molecules in a (5m 5m 4m) room at standard temperature and pressure is of the order of(A) 6 1023

(B) 3 1024

Ans.

(C)

Sol.

PV = N K T

(C) 3 1027

(D) 6 1030

where K is Boltzmann constant

105 100 = N 1.38 10

23

273

N |3 1027

CHEMISTRY31.

Two balloons A and B containing 0.2 mole and 0.1 mole of helium at room temperature and 2.0 atm,respectively, are connected. When equilibrium is established, the final pressure of He in the system is(A) 1.0 atm

(B) 1.5 atm

(C) 0.5 atm

(D) 2.0 atm

Ans.

(D)

Sol.

Since pressure of the gases are same in both the containers. Therefore the final pressure will not change.

32.

In the following set of aromatic compounds

NO2

(i)

COOCH3 OCH3

(ii)

(iii)

(iv)

the correct order of reactivity toward Friedel-Crafts alkylation is

(A) i > ii > iii > iv

(B) ii > iv > iii > i

(C) iv > ii > iii > i

(D) iii > i > iv > ii

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Ans.Sol.

(C)OCH3 is activating group.O

order of deactivating is COCH3 < NO2

33.

The set of principal (n), azimuthal (") and magnetic (m1) quantum numbers that is not allowed for theelectron in H-atom is(A) n = 3, " = 1, m1 = 1

(B) n = 3, " = 0, m1 = 0

(C) n = 2, " = 1, m1 = 0

(D) n = 2, " = 2, m1 = 1

Ans.

(D)

Sol.

n is always greater than "

and m = ".. 0 ..+"

If n = 2, then " = 0, 1and m" = 0, {1, 0, +1}34.

At 298 K, assuming ideal behaviour, the average kinetic energy of a deuterium molecule is(A) two times that of a hydrogen molecule(B) four times that of a hydrogen molecule(C) half of that of a hydrogen molecule(D) same as that of a hydrogen molecule

Ans.

(D)

Sol.

(K.E.)average =

35.

i.e., average kinetic energy depends only on temperature.

As isolated box, equally partitioned contains two ideal gases A and B as shown

3kT2

1 atm, 25C

1 atm, 25C

When the partition is removed, the gases mix. The changes in enthalpy ('H) and entropy ('S) in the process,respectively, are(A) zero, positiveAns.Sol.

(B) zero, negative

(C) positive, zero

(D) negative, zero

(A)According to KTGForce of attraction and repulsion amongst molecules of ideal gas are negligible

The solubility curve of KNO3 in water is shown below.

Solubility (gram)/100 gram of water

The amount of KNO3 that dissolves in 50 g of water at 40C is closest to

(A) 100g

(B) 150g

(C) 200g

Ans.

(A)

Sol.

At 40C solubility is 200 gm per 100 ml (approx)

(D) 50g

i.e., 100 ml of water contains = 200 gm of KNO3(approx)

50 ml of water contains = 100 gm (approx)38.

A compound that shows positive iodoform test is

(A) 2-pentanone

Ans.

(B) 3-pentanone

(C) 3- pentanol

(D) 1-pentanol

(A)

OSol.

(A) CH3CCH2CH2CH3

Show iodoform test

O(B) CH3CH2CCH2CH3(C) CH3CH2CHCH2CH3

OH(D) CH3CH2CH2CH2CH2OH39.

After 2 hours the amount of a certain radioactive substance reduces to 1/16th of the original amount (thedecay process follows first-order kinetics). The half-life of the radioactive substance is(A) 15 min

Ans.

(B) 30 min

(C) 45 min

(D) 60 min

(B)

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Sol.

0.693t1/ 2

a2.303log2 u 60a / 16

t1/2 = 30 min40.

In the conversion of zinc ore to zinc metal, the process of roasting involves(A) ZnCO3 o ZnO

Ans.

(B) ZnO o ZnSO4

(C) ZnS o ZnO

(D) ZnS o ZnSO4

(C)qC2 ZnS + 3O2 950o 2 ZnO + 2 SO2

Sol.

qCo ZnSO4ZnS + 2O2 950

then41.

qC2 ZnSO4 950o 2 ZnO + 2 SO2 + O2

The number of P-H bond(s) in H3PO2, H3PO3 and H3PO4, respectively, is

(A) 2, 0, 1

Ans.

(B) 1, 1, 1

(D) 2, 1, 0

(D)

OSol.

(C) 2, 0, 0

P OH

P OH

HO

OH

P OHOH

So, H3PO2 , H3PO3 and H3PO4 contains 2, 1 and zero PH bonds.

42.

When chlorine gas is passed through an aqueous solution of KBr, the solution turns orange brown due to theformation of(A) KCl

The major product formed in the reaction

Given reaction o SN2

If parents have free ear lobes and the offspring has attached ear lobes, then the parents must be(A) homozygous

Ans.

(B)

47.

During meiosis there is

(B) heterozygous

(C) co-dominant

(D) nullizygous

(A) one round of DNA replication and one division (B) two rounds of DNA replication and one division(C) two rounds of DNA replication and two division (D) one round of DNA replication and two divisionAns.

(D)

Sol.

DNA replication occur in S phase just before to meiosis-I only it will not replicates in between meiosis-I &meiosis-II

48.

Blood clotting involves the conversion of

(A) prothrombin to thromboplastin

(B) thromboplastin to prothrombin

(C) fibrinogen to fibrin

(D) fibrin to fibrinogen

Ans.

(C)

49.

The gall bladder is involved in

(A) synthesizing bile

(B) storing and secreting bile

(C) degrading bile

(D) producing insulin

Ans.

(B)

50.

Which one of the following colours is the LEAST useful for plant life?(A) red

(B) blue

(C) green

Ans.

(C)

51.

At rest the volume of air that moves in and out per breath is called(A) resting volume

(B) vital capacity

(C) lung capacity

(D) tidal volume

Ans.

(D)

52.

How many sex chromosomes does a normal human inherit from father?(A) 1

(B) 2

Ans.

(A)

Sol.

Either X or Y chromosome

(C) 23

(D) violet

(D) 46

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53.

In the 16th century, sailors who travelled long distances had diseases related to malnutrition, because theywere not able to eat fresh vegetables and fruits for months at a time. Scurvy is a result of deficiency of(A) carbohydrates

(B) proteins

Ans.

(C)

54.

The following structure is NOT found in plant cells

(C) Vitamin C

(A) vacuole

(B) nucleus

(C) centriole

(D) endoplasmic reticulum

Ans.

(C)

Sol.

Centriole or centrosome is only present in animal

55.

The cell that transfers information about pain to the brain is called a(A) neuron

(B) blastocyst

(C) histoblast

Ans.

(A)

56.

The presence of nutrients in the food can be tested. Benedict's test is used to detect(A) sucrose

(B) glucose

(C) fatty acid

(D) Vitamin D

(D) haemocyte

(D) vitamin

Ans.

(B)

Sol.

Only reducing sugar give the test with benedict solution.

57.

Several minerals such as iron, iodine, calcium and phosphorous are important nutrients. Iodine is found in(A) thyroxine

lies between 2011, 2011

2

63.

The diameter of one of the bases of a truncated cone is 100 mm. If the diameter of this base is increased by21% such that it still remains a truncated cone with the height and the other base unchanged, the volume alsoincreases by 21%. The radius of the other base (in mm) is(A) 65

Two friends A and B are 30 km apart and they start simultaneously on motorcycles to meet each other. Thespeed of A is 3 times that of B. The distance between them decreases at the rate of 2 km per minute. Tenminutes after they start, A's vehicle breaks down and A stops and waits for B to arrive. After how much time(in minutes) A started riding, does B meet A?(A) 15

Three taps A, B, C fill up a tank independently in 10 hr, 20 hr, 30 hr, respectively. Initially the tank is emptyand exactly one pair of taps is open during each hour and every pair of taps is open at least for one hour.What is the minimum number of hours required to fill the tank?(A) 8

Ans.Sol.

(B) 9

(C) 10

(D) 11

(A)A 10 hrB 20 hrC 30 hrExactly are pair of taps is open during each hour and every pair of taps is open at least for one hour.First A and B are open for 1 hour then B and C and then C and A

1 11 11221 + + =10202030301060

firstsecondthirdth

22 In three hours the tank will be filled part. 60 Now, for minimum time the rest tank must be filled with A and B taps11

10 20

60 th

38 So the rest part of tank will take 5 hours more. 60 So the tank will be filled in 8th hour.

PHYSICS66.

An object with uniform density U is attached to a spring that is known to stretch linearly with applied force asshown below.

When the spring-object system is immersed in a liquid of density U1 as shown in the figure, the springstretches by an amount x1(U > U1). When the experiment is repeated in a liquid of density U2 < U1, the springstretches by an amount x2. Neglecting any buoyant force on the spring, the density of the object is

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(A) U =Ans.

U1x1 U 2 x 2x1 x 2

(B) U =

U1x 2 U 2 x1x 2 x1

(C) U =

U1x 2 U 2 x1x1 x 2

(D) U =

U1x1 U 2 x 2x1 x 2

(B)

Sol.

F.B.D.

U1Vg

kx1 + U1Vg = UVg

(1)

kx2 + U2Vg = UVg

(2)

kx1

U2Vg

kx2

UVg

UVg

from (1) and (2)

U=

67.

U 2 x1 U1x 2x1 x 2

U1x 2 U 2 x1x 2 x1

A body of 0.5 kg moves along the positive x-axis under the influence of a varying force F (in Newtons) asshown below.

F(N)

3210, 0

46x(m)

10

If the speed of the object at x = 4m in 3.16 ms 1 then its speed at x = 8m is

(A) 3.16 ms

(B) 9.3 ms

Ans.

(D)

Sol.

According to work-energy principle

(C) 8 ms

(D) 6.8 ms

WC + Wnc + Wext = 'KE

8

Fdx4

11mvf2 mvi222

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111138 1.5 4 =

[ v f2 (3.16) 2 ]2222vf = 6.8 m/s68.

In a thermally isolated system, two boxes filled with an ideal gas are connected by a valve. When the valve isin closed position, states of the box 1 and 2, respectively, are (1 atm, V, T) and (0.5 atm, 4V, T). When thevalve is opened, the final pressure of the system is approximately(A) 0.5 atm

Ans.

(B) 0.6 atm

(C) 0.75 atm

(D) 1.0 atm

(B)

Sol.

VT1 atm

VT0.5 atm

After opening of at equilibrium temperature and pressure of whole gas is T1 and P1

n1 =

1u V, n2RT

0.5 u V u 4RT

n1 + n2 = nV Vu4

RT 2RT3VRTP1T1

5VP1RT1

5VP1RT10.6T

'Q = 0 ,

'W = 0

? 'U = 0n1CVT + n2CVT = (n1 + n2)CVT1T1 = TP1T

0.6T

P1 = 0.6 atm69.

A student sees the top edge and the bottom center C of a pool simultaneously from an angle T above thehorizontal as shown in the figure. The refraction index of water which fills up to the top edge of the pool is4/3. If h/x = 7/4 then cos T is

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T

hCx

(A)Ans.

27

(B)

(C)

3 45

(D)

3 53

821

(C)T ir

Sol.h

x/2

1 sin i = sin rsin (90 T) =tan r =sin r =

x2h

4sin r3

42=7u2 7

253

428cos T= u=

353 3 53

70.

In the following circuit, the 1 : resistor dissipates power P. If the resistor is replaced by 9:, the powerdissipated in it is:+10V

(A) PAns.

:

(B) 3P

(C) 9P

(D) P/3

(A)

Sol.

3:

10V

1:

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10 = 4ii=

52

255Pi = i2 R = u 1422

100 10 Pf = u 9u912 u 12 12 Pf = Pi

CHEMISTRY71.

An aqueous buffer is prepared by adding 100 ml of 0.1 mol l 1 acetic acid to 50 ml of 0.2 mol l 1 of sodiumacetate. If pKa of acetic acid is 4.76, the pH of the buffer is(A) 4.26

(B) 5.76

(C) 3.76

Ans.

(D)

Sol.

Meq of CH3COOH = 100 0.1 1 = 10

(D) 4.76

Meq of CH3COONa = 50 0.2 1 = 10

pH = pKa + log

[CH 3COO ][CH 3COOH]

pH = 4.76 + log

1010

pH = 4.76 + log 1pH = 4.76

72.

The maximum number of structural isomers possible for the hydrocarbon having the molecular formulaC4H6, is(A) 12

(D) the amount of H2 and I2 will not change

You remove four fresh tobacco leaves of similar size and age. Leave "leaf 1" as it is, smear "leaf 2" withvaseline on the upper surface, "leaf 3" on the lower surface and "leaf 4" on both the surfaces. Hang the leavesfor a few hours and you observe that leaf 1 wilts the most, leaf 2 has wilted, leaf 3 wilted less than leaf 2 andleaf 4 remains fresh. Which of the following conclusion is most logical ?(A) tobacco leaf has more stomata on the upper surface(B) tobacco leaf has more stomata on the lower surface(C) stomata are equally distributed in upper and lower surfaces(D) no conclusion on stomatal distribution can be drawn from this experiment

Ans.

(B)

77.

Vestigial organs such as the appendix exist because

(A) they had an important function during development which is not needed in the adult(B) they have a redundant role to play if an organ with similar function fails(C) nature cannot get rid of structures that have already formed(D) they were inherited from an evolutionary ancestor in which they were functional

Ans.

(D)

78.

Mendel showed that unit factors, now called alleles, exhibit a dominant/ recessive relationship. In amonohybrid cross, the .................. trait disappears in the first filial generation(A) dominant

(B) co-dominant

(C) recessive

(D) semi-dominant

Ans.

(C)

Sol.

Recessive allele does not express itself in presence of dominant allele.

79.

If a man with an X-linked dominant disease has six sons with a woman having a normal complement ofgenes, then the sons will(A) not show any symptoms of the disease(B) show strong symptoms of the disease(C) three will show a disease symptom, while three will not(D) five will show a disease symptom, while one will not

Ans.

(A)

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Sol.

Son get their X chromosome from mother.

80.

In evolutionary terms, an Indian school boys is more closely related to